A LevelSet / XFEM Approach for Topology Optimization of Thermally Loaded Structures

The automotive and aerospace industries use topology optimization to minimize structural weight while satisfying functional constraints. However, the industry-standard fictitious material or density approach has been less effective when applied to physics beyond simple structural mechanics. Known issues include: failed numerical convergence or so-called gray material in computed optimal designs, non-physical responses due to modeling error and spurious contributions to governing equations, and non-trivial extension to design dependent boundary conditions (e.g. radiation, convection, or applied pressure). A comprehensive solution combining the level-set method (LSM) and the extended finite element method (XFEM) enables topology optimization while eliminating fictitious materials by construction. The offerors have successfully applied the LSM-XFEM to structural mechanics, convective heat transfer, nanoscale heat transfer, and several other applications. This Small Business Technology Transfer (STTR) proposal will extend the LSM-XFEM capability of the offerors to include the design of thermally loaded structures including radiation. Previous work addressing ill-conditioning and its effect on displacements and temperatures will be extended to ensure accurate stresses and heat fluxes. The phonon transport equation for nanoscale heat transfer will be extended to the mathematically similar radiative transport equation. Proof of concept thermo-elastic design including radiation using volume and shell elements we be demonstrated.